In a shallow dish, combine the wine with 1 teaspoon of the olive oil and 1/2 teaspoon each of the grainy mustard and rosemary. Add the duck breasts and turn to coat. Cover and refrigerate for 30 minutes.

Meanwhile, bring a medium saucepan of water to a boil. Add the kumquat slices and simmer over moderately high heat until tender, about 5 minutes. Drain the kumquat slices. In the same saucepan, combine the sugar and water and bring to a boil stirring to dissolve the sugar. Add the kumquat slices and simmer over moderate heat for 8 minutes. Transfer the kumquats along with the sugar syrup to a heatproof bowl.

In a large skillet, heat the remaining 1 tablespoon of olive oil. Remove the duck breasts from the marinade; reserve the marinade. Season the duck breasts with salt and pepper and cook over moderately high heat until browned on the bottom, about 3 minutes. Turn the duck breasts, reduce the heat to moderate and cook until browned on the bottom and medium rare, 2 to 3 minutes longer. Transfer the duck breasts to warmed plates.

Add the shallots, jalapeño and remaining 1/2 teaspoon of rosemary to the skillet and cook over moderately low heat until softened, about 4 minutes. Add the reserved duck marinade and simmer over moderately high heat until syrupy, about 3 minutes. Add the kumquats and their syrup and bring to a simmer. Blend in the Dijon mustard and remaining 1 teaspoon of grainy mustard and remove from the heat. Season with salt and pepper. Pour the kumquat sauce over the duck breasts and serve.